# Middle School Math Matters!

A lot rides on your middle school child’s math grades. High school, college, and career may seem far off, but you, your child, and your child’s school are making decisions today that will either open doors down the road, or permanently foreclose certain opportunities.

If your child hopes for a career in science, engineering or math, they will need to complete calculus by the end of high school. In order to be on track to do that, they must complete algebra by the end of eighth grade.

If your child wants to attend Thomas Jefferson or another selective high
school, their path to admission is much harder if they don’t complete algebra
by the end of *seventh grade*.

Dr. Rebecca and Mr. Dan at the *Annandale School for Traditional
Academics* will work with your child to keep them on track to fulfill
their ambitions.

Your child’s first session is free! Call today (571) 549-1100 or email info@annandaleschool.com

## Is Your Child Getting “The Math They Need?”

We see a lot of students who find pre-algebra and algebra challenging.
Algebra is a big change for students. Before middle school math was all about
memorization. Algebra, by contrast, is all about understanding and manipulating
mathematical abstractions. At the *Annandale School*, we focus on helping
students make that leap.

Your child’s school may not be helping them as much as you would think. It seems to be the goal of much modern math teaching to conceal the transition to abstraction. If you pay attention to people who talk about teaching math, you hear a lot about “real world” math, and “giving students the math they really need.”

But what math do they think your children need? One’s ability to split a check or calculate a tip in one’s head is held up as the be-all and end-all of mathematical accomplishment. To this end, much time is wasted on teaching tricks and shortcuts that give your child no insight into the fundamental abstractions that underlie algebra.

Following up on this “real world” approach, the textbooks seek to make math “relevant” by alternating the problems between references to popular culture and exercises in political correctness. Anything but forthrightly to teach your child the abstractions of math.

These teachers play a dirty trick on students. Maybe splitting a check is “all the math your child needs” if they plan to go to a lower-tier college, or not go to college at all; if they plan only to hold menial jobs; if they plan never to have a shot at joining the top tiers of society. But if they are not reconciled to these compromises, they need a traditional education in mathematical abstraction.

When they apply to TJ, what skill do you suppose that test places the most weight on?

When they apply to colleges, what skill does your child need to score well on the math part of the SAT or ACT?

What about the GRE, a high score on which will give them a leg up on getting into the graduate program of their choice, or winning the sweet job they want after college?

You get a gold star if you answered all of these, “the ability to manipulate mathematical abstractions.”

Dr. Rebecca and Mr. Dan at the *Annandale School for Traditional Academics*
will help your child get a solid grounding in the math they will actually need.

Your child’s first session is free! Call today (571) 549-1100 or email info@annandaleschool.com

## Algebra: Abstract, not Abstruse

If your child only needed mathematical abstraction to score well on the TJ test, it would still be something worth learning. But abstraction is much more than that.

People, including math-teacher-people, tend to complain that things are “too abstract,” when we really mean they are “too abstruse.” A topic may be abstruse because it is complicated, confusing, poorly explained, and expressed in cryptic language and symbols. Those don’t make the topic “abstract.”

When we *abstract* a thing, we distill it to its essence. We find a small
number of principles that we can apply to analyze a boundless number of
potential situations. The abstractions that students should be learning in middle
school do not complicate math. They unify and simplify math.

That doesn’t mean that abstraction is easy to learn. Math is hard. Which is why parts of the education establishment so strongly want to avoid having to teach it. But as hard as it is, it is something that most people can learn, and having learned it, will find very useful.

A little bit of algebraic abstraction replaces an enormous amount of memorization. Before algebra, math students memorize recipes. Early in elementary school, we learned the “standard algorithm” for multiplying integers. Then we learned a modified version for decimals. And another recipe for multiplying fractions. Eventually, we learned F.O.I.L for multiplying binomials, then we learned to multiply polynomials, and so on.

Around middle school, a student starts to be overwhelmed by the shear quantity of recipes they have been asked to remember. That’s when they need abstraction. For example, all of the different algorithms for multiplication that we listed before are really expressions of a single underlying abstract principle: the distributive property. Once a student understands that the distributive property, applied to each of these different situations, leads to each of these different algorithms, it becomes much easier to keep track of the algorithms and when to use them.

Not coincidentally, in middle school some students emerge as “math geniuses.” There is a misconception that such students have an unusual talent for memorization. In fact, the opposite may be the case. A student who is unusually good at memorizing recipes may fail to make the transition to abstraction when they need to. Eventually, even that student will be overwhelmed by the encyclopedia of recipes they are asked to memorize.

The student who has only an average ability to memorize is in more immediate trouble. Without help from the powerful abstractions of algebra, they will end up at one of two places. Either, they will work hard and still be unable to keep up, or they will perceive the hopelessness of their task, and give up trying. Such students are called, respectively (and unfairly), “stupid” or “lazy.”

The “math genius,” on the other hand, may not be a genius, and may not work particularly hard. They are someone who stumbled into the realization that, if they remember a small number of basic principles, they can get away without memorizing most of the recipes the teacher gives them in class.

Dr. Rebecca and Mr. Dan at the *Annandale School for Traditional Academics*
will help your child find their inner math genius.

Your child’s first session is free! Call today (571) 549-1100 or email info@annandaleschool.com

## Tutoring from Math Experts in Annandale

We teach Pre-algebra, Algebra, Geometry, Trigonometry, Pre-calculus, Calculus, Discrete math, Statistics, Economics, Physics, Chemistry.

Rebecca and Dan at the Annandale School are experienced professionals. Turn to us when you want the best. Help improve grades and prepare for tests.

We help students in middle school, high school and college.

We assess your child’s skills to pinpoint the areas that are causing them the most trouble.

New students receive a free assessment and free one hour session.

Your child’s first session is free! Call today (571) 549-1100 or email info@annandaleschool.com